Nonlinear Dynamics of Spinning Bosonic Stars: Formation and Stability

Abstract

We perform numerical evolutions of the fully non-linear Einstein-(complex, massive) Klein-Gordon and Einstein-(complex) Proca systems, to assess the formation and stability of spinning bosonic stars. In the scalar/vector case these are known as boson/Proca stars. Firstly, we consider the formation scenario. Starting with constraint-obeying initial data, describing a dilute, axisymmetric cloud of spinning scalar/Proca field, gravitational collapse towards a spinning star occurs, via gravitational cooling. In the scalar case the formation is transient, even for a non-perturbed initial cloud; a non-axisymmetric instability always develops ejecting all the angular momentum from the scalar star. In the Proca case, by contrast, no instability is observed and the evolutions are compatible with the formation of a spinning Proca star. Secondly, we address the stability of an existing star, a stationary solution of the field equations. In the scalar case, a non-axisymmetric perturbation develops collapsing the star to a spinning black hole. No such instability is found in the Proca case, where the star survives large amplitude perturbations; moreover, some excited Proca stars decay to, and remain as, fundamental states. Our analysis suggests bosonic stars have different stability properties in the scalar/vector case, which we tentatively relate to their toroidal/spheroidal morphology. A parallelism with instabilities of spinning fluid stars is briefly discussed.

Perturbing the ground state of Dirac stars

“…Solutions for spinning Dirac stars were recently found [29]. A stability analysis for such solutions, which has recently been initiated for spinning boson and Proca stars [40], would be interesting. The spherically symmetric Dirac spinor ansatz we presented in (31) does not have the same form as found elsewhere in the literature [1,18,23] but, as we show here, it is equivalent.…”

Self-interacting multistate boson stars

“…The study of BSs can be extended to the case of charged BSs [31][32][33], nonrotating and rotating axion boson stars [34,35], Proca stars [36][37][38], and in the higher-dimensional spacetime case [39]. The linear stability of boson stars with respect to small oscillations was discussed by Lee and Pang in [40], the study of the stability properties of boson stars extended to the quartic and sextic self-interaction term case [41], dynamical -BSs [42,43], and non-linear dynamics of spinning BSs case [44]. The properties of BSs have been investigated widely [45][46][47][48][49][50][51][52][53][54][55].…”

Black holes with synchronised Proca hair: linear clouds and fundamental non-linear solutions

“…The second goal of this paper is, therefore, to report a detailed study of the fundamental solutions of these hairy BHs. In particular, their solitonic limit corresponds precisely to the solutions that have been recently shown to be dynamically robust [17] -see also [48].…”

“…Proca stars [16]. Very recently, it has been shown that the spinning scalar stars suffer from a non-axisymmetric instability, whereas the spinning Proca stars are dynamically robust [17]. This suggests that the Proca case may be dynamically more interesting.…”